Biomedical Engineering Reference
In-Depth Information
factors are defined with a dependency on the ratio of ionic solute radius to
the preexisting pore radius, λ = r/r P .
Often, for simplification, studies rely on a pore model in which the pores
are represented by a single average pore radius value (Higuchi et al. 1999; Li
et al. 2004). For instance, Higuchi et al. (1999) assumed that the lipid bilayers
membranes of the SC have small pores of preexisting radii in the range 10
r P
20A. Under this approximation, direct descriptions of the diffusive hindrance
and hydrodynamic hindrance are applicable (Deen 1987). Two regimes based on
the magnitude of this ratio are commonly put into practice.
For medium and small molecule transport ( λ< 0 . 4), hindrance factors are
represented by
λ ) 2 1
0 . 948 λ 5
2 . 104 λ +2 . 09 λ 3
H ( λ )=(1
(9.13)
λ ) 2 ) 1
0 . 163 λ 3
λ ) 2 (2
0 . 667 λ 2
W ( λ )=(1
(1
(9.14)
while large solute particles (0 . 4
λ ) have the associated hindrance factor
relations:
H ( λ )= 6 π (1 λ ) 2
K t
(9.15)
λ ) 2 (2
λ ) 2 ) K s
W ( λ )= (1
(1
(9.16)
2 K t
where
λ ) 5 / 2 1+
λ ) n +
K s
K t
= 9
a n
b n
(1
a n +3
b n +3
λ n
2
4
4 π 2 2(1
n =1
n =0
(9.17)
and
a 1 =
1 . 217;
a 2 =1 . 534;
a 3 =
22 . 51;
a 4 =
5 . 612;
a 5 =
0 . 3363;
a 6 =
1 . 216;
a 7 =1 . 647;
b 1 =0 . 1167;
b 2 =
0 . 04419;
b 3 =4 . 018;
b 4 =
3 . 979;
b 5 =
1 . 922;
b 6 =4 . 392;
b 7 =5 . 006
However, in the case of a distribution of pore radii within the skin, a
distributive function, γ ( r P ), is applied and the hindrance factor is defined as
H =
γ ( r P ) H ( λ ) dr P
(9.18)
0
 
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